The version of MySQL in Zimbra uses a non-standard port so it shouldn't cause you problems. The only one that will is Port 80 for you current Apache install. When you install Zimbra it will check for port conflicts and allow you to change the number in Zimbra.

You should have no problems as long as you change the zimbra ports at install time, go through the menu before you commit the install and check everything and change what you need. Have a search of the forums for related questions on this subject.